GeographicLib
1.21
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Azimuthal Equidistant Projection. More...
#include <GeographicLib/AzimuthalEquidistant.hpp>
Public Member Functions | |
AzimuthalEquidistant (const Geodesic &earth=Geodesic::WGS84) throw () | |
void | Forward (real lat0, real lon0, real lat, real lon, real &x, real &y, real &azi, real &rk) const throw () |
void | Reverse (real lat0, real lon0, real x, real y, real &lat, real &lon, real &azi, real &rk) const throw () |
void | Forward (real lat0, real lon0, real lat, real lon, real &x, real &y) const throw () |
void | Reverse (real lat0, real lon0, real x, real y, real &lat, real &lon) const throw () |
Inspector functions | |
Math::real | MajorRadius () const throw () |
Math::real | Flattening () const throw () |
Azimuthal Equidistant Projection.
Azimuthal equidistant projection centered at an arbitrary position on the ellipsoid. For a point in projected space (x, y), the geodesic distance from the center position is hypot(x, y) and the azimuth of the geodesic from the center point is atan2(x, y). The Forward and Reverse methods also return the azimuth azi of the geodesic at (x, y) and reciprocal scale rk in the azimuthal direction which, together with the basic properties of the projection, serve to specify completely the local affine transformation between geographic and projected coordinates.
The conversions all take place using a Geodesic object (by default Geodesic::WGS84). For more information on geodesics see Geodesics on the ellipsoid.
Example of use:
// Example of using the GeographicLib::AzimuthalEquidistant class // $Id: d018fda4dc3289b06b9e6fe8cda16638430d9213 $ #include <iostream> #include <exception> #include <GeographicLib/Geodesic.hpp> #include <GeographicLib/AzimuthalEquidistant.hpp> using namespace std; using namespace GeographicLib; int main() { try { Geodesic geod(Constants::WGS84_a(), Constants::WGS84_f()); // Alternatively: const Geodesic& geod = Geodesic::WGS84; const double lat0 = 48 + 50/60.0, lon0 = 2 + 20/60.0; // Paris AzimuthalEquidistant proj(geod); { // Sample forward calculation double lat = 50.9, lon = 1.8; // Calais double x, y; proj.Forward(lat0, lon0, lat, lon, x, y); cout << x << " " << y << "\n"; } { // Sample reverse calculation double x = -38e3, y = 230e3; double lat, lon; proj.Reverse(lat0, lon0, x, y, lat, lon); cout << lat << " " << lon << "\n"; } } catch (const exception& e) { cerr << "Caught exception: " << e.what() << "\n"; return 1; } return 0; }
GeodesicProj is a command-line utility providing access to the functionality of AzimuthalEquidistant, Gnomonic, and CassiniSoldner.
GeographicLib::AzimuthalEquidistant::AzimuthalEquidistant | ( | const Geodesic & | earth = Geodesic::WGS84 | ) | throw () [inline, explicit] |
Constructor for AzimuthalEquidistant.
[in] | earth | the Geodesic object to use for geodesic calculations. By default this uses the WGS84 ellipsoid. |
Definition at line 56 of file AzimuthalEquidistant.hpp.
void GeographicLib::AzimuthalEquidistant::Forward | ( | real | lat0, |
real | lon0, | ||
real | lat, | ||
real | lon, | ||
real & | x, | ||
real & | y, | ||
real & | azi, | ||
real & | rk | ||
) | const throw () |
Forward projection, from geographic to azimuthal equidistant.
[in] | lat0 | latitude of center point of projection (degrees). |
[in] | lon0 | longitude of center point of projection (degrees). |
[in] | lat | latitude of point (degrees). |
[in] | lon | longitude of point (degrees). |
[out] | x | easting of point (meters). |
[out] | y | northing of point (meters). |
[out] | azi | azimuth of geodesic at point (degrees). |
[out] | rk | reciprocal of azimuthal scale at point. |
lat0 and lat should be in the range [-90, 90] and lon0 and lon should be in the range [-180, 360]. The scale of the projection is 1 in the "radial" direction, azi clockwise from true north, and is 1/rk in the direction perpendicular to this. A call to Forward followed by a call to Reverse will return the original (lat, lon) (to within roundoff).
Definition at line 25 of file AzimuthalEquidistant.cpp.
Referenced by main().
void GeographicLib::AzimuthalEquidistant::Reverse | ( | real | lat0, |
real | lon0, | ||
real | x, | ||
real | y, | ||
real & | lat, | ||
real & | lon, | ||
real & | azi, | ||
real & | rk | ||
) | const throw () |
Reverse projection, from azimuthal equidistant to geographic.
[in] | lat0 | latitude of center point of projection (degrees). |
[in] | lon0 | longitude of center point of projection (degrees). |
[in] | x | easting of point (meters). |
[in] | y | northing of point (meters). |
[out] | lat | latitude of point (degrees). |
[out] | lon | longitude of point (degrees). |
[out] | azi | azimuth of geodesic at point (degrees). |
[out] | rk | reciprocal of azimuthal scale at point. |
lat0 should be in the range [-90, 90] and lon0 should be in the range [-180, 360]. lat will be in the range [-90, 90] and lon will be in the range [-180, 180). The scale of the projection is 1 in the "radial" direction, azi clockwise from true north, and is 1/rk in the direction perpendicular to this. A call to Reverse followed by a call to Forward will return the original (x, y) (to roundoff) only if the geodesic to (x, y) is a shortest path.
Definition at line 36 of file AzimuthalEquidistant.cpp.
Referenced by main().
void GeographicLib::AzimuthalEquidistant::Forward | ( | real | lat0, |
real | lon0, | ||
real | lat, | ||
real | lon, | ||
real & | x, | ||
real & | y | ||
) | const throw () [inline] |
AzimuthalEquidistant::Forward without returning the azimuth and scale.
Definition at line 107 of file AzimuthalEquidistant.hpp.
void GeographicLib::AzimuthalEquidistant::Reverse | ( | real | lat0, |
real | lon0, | ||
real | x, | ||
real | y, | ||
real & | lat, | ||
real & | lon | ||
) | const throw () [inline] |
AzimuthalEquidistant::Reverse without returning the azimuth and scale.
Definition at line 116 of file AzimuthalEquidistant.hpp.
Math::real GeographicLib::AzimuthalEquidistant::MajorRadius | ( | ) | const throw () [inline] |
Definition at line 129 of file AzimuthalEquidistant.hpp.
Math::real GeographicLib::AzimuthalEquidistant::Flattening | ( | ) | const throw () [inline] |
Definition at line 135 of file AzimuthalEquidistant.hpp.